High-temperature superconducting (HTS) coils made of coated conductors that can operate in persistent current mode (PCM) are regarded to be promising in MRI/nuclear magnetic resonance and Maglev system. The temporal stability of the magnetic field trapped by the PCM coil is a key issue, which significantly determines the imaging quality of MRI and dynamic behavior of Maglev. This study focuses on the temporal stability of the trapped magnetic field in the double-slit HTS PCM coil, which is magnetized by a field cooling (FC) method at 77 K. The magnetic field decay behavior under different initial fields and FC ramp rates are systematically studied. The experiment results indicate that higher initially trapped field will lead to faster decay, but if the initially trapped field is lower than a certain value, this trend is no longer obvious. The FC ramp rate has a little impact on the field decay. Finally, a numerical model based on R-L circuit and E-J equation is established to fit the decay process. It is found that if the operating current is lower than 60% of the coil critical current, good temporal stability could be achieved. Another long-term experiment is performed that a stability of 8.1 ppm/h is achieved after 19 days' decay.